plot-methods: Plot method for performance objects
In ROCR: Visualizing the Performance of Scoring Classifiers
Description
Usage
Arguments
Author(s)
References
See Also
Examples
Description
This is the method to plot all objects of class performance.
Usage
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## S4 method for signature 'performance,missing'
plot(
x,
y,
...,
avg = "none",
spread.estimate = "none",
spread.scale = 1,
show.spread.at = c(),
colorize = FALSE,
colorize.palette = rev(rainbow(256, start = 0, end = 4/6)),
colorkey = colorize,
colorkey.relwidth = 0.25,
colorkey.pos = "right",
print.cutoffs.at = c(),
cutoff.label.function = function(x) { round(x, 2) },
downsampling = 0,
add = FALSE
)
## S3 method for class 'performance'
plot(...)
Arguments
x
an object of class performance
y
not used
...
Optional graphical parameters to adjust different components of
the performance plot. Parameters are directed to their target component by
prefixing them with the name of the component (component.parameter,
e.g. text.cex). The following components are available:
xaxis, yaxis, coloraxis, box (around the
plotting region), points, text, plotCI (error bars),
boxplot. The names of these components are influenced by the R
functions that are used to create them. Thus, par(component) can be
used to see which parameters are available for a given component (with the
expection of the three axes; use par(axis) here). To adjust the
canvas or the performance curve(s), the standard plot parameters can
be used without any prefix.
avg
If the performance object describes several curves (from
cross-validation runs or bootstrap evaluations of one particular method),
the curves from each of the runs can be averaged. Allowed values are
none (plot all curves separately), horizontal (horizontal
averaging), vertical (vertical averaging), and threshold
(threshold (=cutoff) averaging). Note that while threshold averaging is
always feasible, vertical and horizontal averaging are not well-defined if
the graph cannot be represented as a function x->y and y->x, respectively.
spread.estimate
When curve averaging is enabled, the variation around
the average curve can be visualized as standard error bars
(stderror), standard deviation bars (stddev), or by using box
plots (boxplot). Note that the function plotCI, which is used
internally by ROCR to draw error bars, might raise a warning if the spread
of the curves at certain positions is 0.
spread.scale
For stderror or stddev, this is a scalar
factor to be multiplied with the length of the standard error/deviation
bar. For example, under normal assumptions, spread.scale=2 can be
used to get approximate 95% confidence intervals.
show.spread.at
For vertical averaging, this vector determines the x
positions for which the spread estimates should be visualized. In contrast,
for horizontal and threshold averaging, the y positions and cutoffs are
determined, respectively. By default, spread estimates are shown at 11
equally spaced positions.
colorize
This logical determines whether the curve(s) should be
colorized according to cutoff.
colorize.palette
If curve colorizing is enabled, this determines the
color palette onto which the cutoff range is mapped.
colorkey
If true, a color key is drawn into the 4% border
region (default of par(xaxs) and par(yaxs)) of the
plot. The color key visualizes the mapping from cutoffs to colors.
colorkey.relwidth
Scalar between 0 and 1 that determines the
fraction of the 4% border region that is occupied by the colorkey.
colorkey.pos
Determines if the colorkey is drawn vertically at
the right side, or horizontally at the top of the
plot.
print.cutoffs.at
This vector specifies the cutoffs which should
be printed as text along the curve at the corresponding curve positions.
cutoff.label.function
By default, cutoff annotations along the curve
or at the color key are rounded to two decimal places before printing.
Using a custom cutoff.label.function, any other transformation can
be performed on the cutoffs instead (e.g. rounding with different precision
or taking the logarithm).
downsampling
ROCR can efficiently compute most performance measures
even for data sets with millions of elements. However, plotting of large
data sets can be slow and lead to PS/PDF documents of considerable size. In
that case, performance curves that are indistinguishable from the original
can be obtained by using only a fraction of the computed performance
values. Values for downsampling between 0 and 1 indicate the fraction of
the original data set size to which the performance object should be
downsampled, integers above 1 are interpreted as the actual number of
performance values to which the curve(s) should be downsampled.
add
If TRUE, the curve(s) is/are added to an already existing
plot; otherwise a new plot is drawn.
Author(s)
Tobias Sing tobias.sing@gmail.com, Oliver Sander
osander@gmail.com
References
A detailed list of references can be found on the ROCR homepage at
http://rocr.bioinf.mpi-sb.mpg.de.
See Also
prediction,
performance,
prediction-class,
performance-class
Examples
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# plotting a ROC curve:
library(ROCR)
data(ROCR.simple)
pred <- prediction( ROCR.simple$predictions, ROCR.simple$labels )
pred
perf <- performance( pred, "tpr", "fpr" )
perf
plot( perf )
# To entertain your children, make your plots nicer
# using ROCR's flexible parameter passing mechanisms
# (much cheaper than a finger painting set)
par(bg="lightblue", mai=c(1.2,1.5,1,1))
plot(perf, main="ROCR fingerpainting toolkit", colorize=TRUE,
xlab="Mary's axis", ylab="", box.lty=7, box.lwd=5,
box.col="gold", lwd=17, colorkey.relwidth=0.5, xaxis.cex.axis=2,
xaxis.col='blue', xaxis.col.axis="blue", yaxis.col='green', yaxis.cex.axis=2,
yaxis.at=c(0,0.5,0.8,0.85,0.9,1), yaxis.las=1, xaxis.lwd=2, yaxis.lwd=3,
yaxis.col.axis="orange", cex.lab=2, cex.main=2)
Example output
Loading required package: gplots
Attaching package: 'gplots'
The following object is masked from 'package:stats':
lowess
An object of class "prediction"
Slot "predictions":
[[1]]
[1] 0.612547843 0.364270971 0.432136142 0.140291078 0.384895941 0.244415489
[7] 0.970641299 0.890172812 0.781781371 0.868751832 0.716680598 0.360168796
[13] 0.547983407 0.385240464 0.423739359 0.101699993 0.628095575 0.744769966
[19] 0.657732644 0.490119891 0.072369921 0.172741714 0.105722115 0.890078186
[25] 0.945548941 0.984667270 0.360180429 0.448687336 0.014823599 0.543533783
[31] 0.292368449 0.701561487 0.715459280 0.714985914 0.120604738 0.319672178
[37] 0.911723615 0.757325590 0.090988280 0.529402244 0.257402979 0.589909284
[43] 0.708412104 0.326672910 0.086546283 0.879459891 0.362693564 0.230157183
[49] 0.779771989 0.876086217 0.353281048 0.212014560 0.703293499 0.689075677
[55] 0.627012496 0.240911145 0.402801992 0.134794140 0.120473353 0.665444679
[61] 0.536339509 0.623494622 0.885179651 0.353777439 0.408939895 0.265686095
[67] 0.932159806 0.248500489 0.858876675 0.491735594 0.151350957 0.694457482
[73] 0.496513160 0.123504905 0.499788081 0.310718619 0.907651100 0.340078180
[79] 0.195097957 0.371936985 0.517308606 0.419560072 0.865639036 0.018527600
[85] 0.539086009 0.005422562 0.772728821 0.703885141 0.348213542 0.277656869
[91] 0.458674210 0.059045866 0.133257805 0.083685883 0.531958184 0.429650397
[97] 0.717845453 0.537091350 0.212404891 0.930846938 0.083048377 0.468610247
[103] 0.393378108 0.663367560 0.349540913 0.194398425 0.844415442 0.959417835
[109] 0.211378771 0.943432189 0.598162949 0.834803976 0.576836208 0.380396459
[115] 0.161874325 0.912325837 0.642933593 0.392173971 0.122284044 0.586857799
[121] 0.180631658 0.085993218 0.700501359 0.060413627 0.531464015 0.084254795
[127] 0.448484671 0.938583020 0.531006532 0.785213140 0.905121019 0.748438143
[133] 0.605235403 0.842974300 0.835981859 0.364288579 0.492596896 0.488179708
[139] 0.259278968 0.991096434 0.757364019 0.288258273 0.773336236 0.040906997
[145] 0.110241034 0.760726142 0.984599159 0.253271061 0.697235328 0.620501132
[151] 0.814586047 0.300973098 0.378092079 0.016694412 0.698826511 0.658692553
[157] 0.470206008 0.501489336 0.239143340 0.050999138 0.088450984 0.107031842
[163] 0.746588080 0.480100183 0.336592126 0.579511087 0.118555284 0.233160827
[169] 0.461150807 0.370549294 0.770178504 0.537336015 0.463227453 0.790240205
[175] 0.883431431 0.745110673 0.007746305 0.012653524 0.868331219 0.439399995
[181] 0.540221346 0.567043171 0.035815400 0.806543942 0.248707470 0.696702150
[187] 0.081439129 0.336315317 0.126480399 0.636728451 0.030235062 0.268138293
[193] 0.983494405 0.728536415 0.739554341 0.522384507 0.858970526 0.383807972
[199] 0.606960209 0.138387070
Slot "labels":
[[1]]
[1] 1 1 0 0 0 1 1 1 1 0 1 0 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0 1 1 0 1 1 1 0 0 1
[38] 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 0 0 0 1 0 1 0 0 1 0 0
[75] 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 0 1 0 0 1 0 0 1 1
[112] 1 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 1 1 0 1 0 1 0 1 1
[149] 1 1 1 0 0 0 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 0
[186] 0 0 1 0 0 0 1 0 1 1 0 1 0 1 0
Levels: 0 < 1
Slot "cutoffs":
[[1]]
[1] Inf 0.991096434 0.984667270 0.984599159 0.983494405 0.970641299
[7] 0.959417835 0.945548941 0.943432189 0.938583020 0.932159806 0.930846938
[13] 0.912325837 0.911723615 0.907651100 0.905121019 0.890172812 0.890078186
[19] 0.885179651 0.883431431 0.879459891 0.876086217 0.868751832 0.868331219
[25] 0.865639036 0.858970526 0.858876675 0.844415442 0.842974300 0.835981859
[31] 0.834803976 0.814586047 0.806543942 0.790240205 0.785213140 0.781781371
[37] 0.779771989 0.773336236 0.772728821 0.770178504 0.760726142 0.757364019
[43] 0.757325590 0.748438143 0.746588080 0.745110673 0.744769966 0.739554341
[49] 0.728536415 0.717845453 0.716680598 0.715459280 0.714985914 0.708412104
[55] 0.703885141 0.703293499 0.701561487 0.700501359 0.698826511 0.697235328
[61] 0.696702150 0.694457482 0.689075677 0.665444679 0.663367560 0.658692553
[67] 0.657732644 0.642933593 0.636728451 0.628095575 0.627012496 0.623494622
[73] 0.620501132 0.612547843 0.606960209 0.605235403 0.598162949 0.589909284
[79] 0.586857799 0.579511087 0.576836208 0.567043171 0.547983407 0.543533783
[85] 0.540221346 0.539086009 0.537336015 0.537091350 0.536339509 0.531958184
[91] 0.531464015 0.531006532 0.529402244 0.522384507 0.517308606 0.501489336
[97] 0.499788081 0.496513160 0.492596896 0.491735594 0.490119891 0.488179708
[103] 0.480100183 0.470206008 0.468610247 0.463227453 0.461150807 0.458674210
[109] 0.448687336 0.448484671 0.439399995 0.432136142 0.429650397 0.423739359
[115] 0.419560072 0.408939895 0.402801992 0.393378108 0.392173971 0.385240464
[121] 0.384895941 0.383807972 0.380396459 0.378092079 0.371936985 0.370549294
[127] 0.364288579 0.364270971 0.362693564 0.360180429 0.360168796 0.353777439
[133] 0.353281048 0.349540913 0.348213542 0.340078180 0.336592126 0.336315317
[139] 0.326672910 0.319672178 0.310718619 0.300973098 0.292368449 0.288258273
[145] 0.277656869 0.268138293 0.265686095 0.259278968 0.257402979 0.253271061
[151] 0.248707470 0.248500489 0.244415489 0.240911145 0.239143340 0.233160827
[157] 0.230157183 0.212404891 0.212014560 0.211378771 0.195097957 0.194398425
[163] 0.180631658 0.172741714 0.161874325 0.151350957 0.140291078 0.138387070
[169] 0.134794140 0.133257805 0.126480399 0.123504905 0.122284044 0.120604738
[175] 0.120473353 0.118555284 0.110241034 0.107031842 0.105722115 0.101699993
[181] 0.090988280 0.088450984 0.086546283 0.085993218 0.084254795 0.083685883
[187] 0.083048377 0.081439129 0.072369921 0.060413627 0.059045866 0.050999138
[193] 0.040906997 0.035815400 0.030235062 0.018527600 0.016694412 0.014823599
[199] 0.012653524 0.007746305 0.005422562
Slot "fp":
[[1]]
[1] 0 0 0 0 1 1 2 3 3 3 3 3 3 3 4 4 4 4
[19] 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5
[37] 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 8
[55] 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12
[73] 12 12 12 13 13 13 13 13 14 14 14 14 14 15 15 15 15 15
[91] 15 15 15 16 16 16 17 18 19 20 21 22 23 24 25 26 27 28
[109] 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
[127] 47 47 48 49 50 51 51 52 53 54 55 55 55 56 57 58 59 60
[145] 60 60 61 62 63 63 64 65 65 66 67 68 68 69 70 71 72 73
[163] 74 75 76 77 78 79 80 80 81 82 83 84 85 86 86 87 88 89
[181] 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 106
[199] 106 107 107
Slot "tp":
[[1]]
[1] 0 1 2 3 3 4 4 4 5 6 7 8 9 10 10 11 12 13 14 15 16 17 17 18 19
[26] 20 21 22 23 24 25 26 27 28 29 30 30 31 32 33 33 34 35 36 37 38 39 40 41 42
[51] 43 44 45 45 45 46 47 48 49 50 50 51 51 52 53 54 55 56 56 57 58 59 60 61 62
[76] 62 63 64 65 66 66 67 68 69 70 70 71 72 73 74 75 76 77 77 78 79 79 79 79 79
[101] 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79
[126] 79 79 80 80 80 80 80 81 81 81 81 81 82 83 83 83 83 83 83 84 85 85 85 85 86
[151] 86 86 87 87 87 87 88 88 88 88 88 88 88 88 88 88 88 88 88 89 89 89 89 89 89
[176] 89 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 91 92 92
[201] 93
Slot "tn":
[[1]]
[1] 107 107 107 107 106 106 105 104 104 104 104 104 104 104 103 103 103 103
[19] 103 103 103 103 102 102 102 102 102 102 102 102 102 102 102 102 102 102
[37] 101 101 101 101 100 100 100 100 100 100 100 100 100 100 100 100 100 99
[55] 98 98 98 98 98 98 97 97 96 96 96 96 96 96 95 95 95 95
[73] 95 95 95 94 94 94 94 94 93 93 93 93 93 92 92 92 92 92
[91] 92 92 92 91 91 91 90 89 88 87 86 85 84 83 82 81 80 79
[109] 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61
[127] 60 60 59 58 57 56 56 55 54 53 52 52 52 51 50 49 48 47
[145] 47 47 46 45 44 44 43 42 42 41 40 39 39 38 37 36 35 34
[163] 33 32 31 30 29 28 27 27 26 25 24 23 22 21 21 20 19 18
[181] 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 1
[199] 1 0 0
Slot "fn":
[[1]]
[1] 93 92 91 90 90 89 89 89 88 87 86 85 84 83 83 82 81 80 79 78 77 76 76 75 74
[26] 73 72 71 70 69 68 67 66 65 64 63 63 62 61 60 60 59 58 57 56 55 54 53 52 51
[51] 50 49 48 48 48 47 46 45 44 43 43 42 42 41 40 39 38 37 37 36 35 34 33 32 31
[76] 31 30 29 28 27 27 26 25 24 23 23 22 21 20 19 18 17 16 16 15 14 14 14 14 14
[101] 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14
[126] 14 14 13 13 13 13 13 12 12 12 12 12 11 10 10 10 10 10 10 9 8 8 8 8 7
[151] 7 7 6 6 6 6 5 5 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4
[176] 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 1 1
[201] 0
Slot "n.pos":
[[1]]
[1] 93
Slot "n.neg":
[[1]]
[1] 107
Slot "n.pos.pred":
[[1]]
[1] 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
[19] 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
[37] 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53
[55] 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71
[73] 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89
[91] 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107
[109] 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125
[127] 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143
[145] 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161
[163] 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179
[181] 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197
[199] 198 199 200
Slot "n.neg.pred":
[[1]]
[1] 200 199 198 197 196 195 194 193 192 191 190 189 188 187 186 185 184 183
[19] 182 181 180 179 178 177 176 175 174 173 172 171 170 169 168 167 166 165
[37] 164 163 162 161 160 159 158 157 156 155 154 153 152 151 150 149 148 147
[55] 146 145 144 143 142 141 140 139 138 137 136 135 134 133 132 131 130 129
[73] 128 127 126 125 124 123 122 121 120 119 118 117 116 115 114 113 112 111
[91] 110 109 108 107 106 105 104 103 102 101 100 99 98 97 96 95 94 93
[109] 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75
[127] 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57
[145] 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39
[163] 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21
[181] 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3
[199] 2 1 0
An object of class "performance"
Slot "x.name":
[1] "False positive rate"
Slot "y.name":
[1] "True positive rate"
Slot "alpha.name":
[1] "Cutoff"
Slot "x.values":
[[1]]
[1] 0.000000000 0.000000000 0.000000000 0.000000000 0.009345794 0.009345794
[7] 0.018691589 0.028037383 0.028037383 0.028037383 0.028037383 0.028037383
[13] 0.028037383 0.028037383 0.037383178 0.037383178 0.037383178 0.037383178
[19] 0.037383178 0.037383178 0.037383178 0.037383178 0.046728972 0.046728972
[25] 0.046728972 0.046728972 0.046728972 0.046728972 0.046728972 0.046728972
[31] 0.046728972 0.046728972 0.046728972 0.046728972 0.046728972 0.046728972
[37] 0.056074766 0.056074766 0.056074766 0.056074766 0.065420561 0.065420561
[43] 0.065420561 0.065420561 0.065420561 0.065420561 0.065420561 0.065420561
[49] 0.065420561 0.065420561 0.065420561 0.065420561 0.065420561 0.074766355
[55] 0.084112150 0.084112150 0.084112150 0.084112150 0.084112150 0.084112150
[61] 0.093457944 0.093457944 0.102803738 0.102803738 0.102803738 0.102803738
[67] 0.102803738 0.102803738 0.112149533 0.112149533 0.112149533 0.112149533
[73] 0.112149533 0.112149533 0.112149533 0.121495327 0.121495327 0.121495327
[79] 0.121495327 0.121495327 0.130841121 0.130841121 0.130841121 0.130841121
[85] 0.130841121 0.140186916 0.140186916 0.140186916 0.140186916 0.140186916
[91] 0.140186916 0.140186916 0.140186916 0.149532710 0.149532710 0.149532710
[97] 0.158878505 0.168224299 0.177570093 0.186915888 0.196261682 0.205607477
[103] 0.214953271 0.224299065 0.233644860 0.242990654 0.252336449 0.261682243
[109] 0.271028037 0.280373832 0.289719626 0.299065421 0.308411215 0.317757009
[115] 0.327102804 0.336448598 0.345794393 0.355140187 0.364485981 0.373831776
[121] 0.383177570 0.392523364 0.401869159 0.411214953 0.420560748 0.429906542
[127] 0.439252336 0.439252336 0.448598131 0.457943925 0.467289720 0.476635514
[133] 0.476635514 0.485981308 0.495327103 0.504672897 0.514018692 0.514018692
[139] 0.514018692 0.523364486 0.532710280 0.542056075 0.551401869 0.560747664
[145] 0.560747664 0.560747664 0.570093458 0.579439252 0.588785047 0.588785047
[151] 0.598130841 0.607476636 0.607476636 0.616822430 0.626168224 0.635514019
[157] 0.635514019 0.644859813 0.654205607 0.663551402 0.672897196 0.682242991
[163] 0.691588785 0.700934579 0.710280374 0.719626168 0.728971963 0.738317757
[169] 0.747663551 0.747663551 0.757009346 0.766355140 0.775700935 0.785046729
[175] 0.794392523 0.803738318 0.803738318 0.813084112 0.822429907 0.831775701
[181] 0.841121495 0.850467290 0.859813084 0.869158879 0.878504673 0.887850467
[187] 0.897196262 0.906542056 0.915887850 0.925233645 0.934579439 0.943925234
[193] 0.953271028 0.962616822 0.971962617 0.981308411 0.990654206 0.990654206
[199] 0.990654206 1.000000000 1.000000000
Slot "y.values":
[[1]]
[1] 0.00000000 0.01075269 0.02150538 0.03225806 0.03225806 0.04301075
[7] 0.04301075 0.04301075 0.05376344 0.06451613 0.07526882 0.08602151
[13] 0.09677419 0.10752688 0.10752688 0.11827957 0.12903226 0.13978495
[19] 0.15053763 0.16129032 0.17204301 0.18279570 0.18279570 0.19354839
[25] 0.20430108 0.21505376 0.22580645 0.23655914 0.24731183 0.25806452
[31] 0.26881720 0.27956989 0.29032258 0.30107527 0.31182796 0.32258065
[37] 0.32258065 0.33333333 0.34408602 0.35483871 0.35483871 0.36559140
[43] 0.37634409 0.38709677 0.39784946 0.40860215 0.41935484 0.43010753
[49] 0.44086022 0.45161290 0.46236559 0.47311828 0.48387097 0.48387097
[55] 0.48387097 0.49462366 0.50537634 0.51612903 0.52688172 0.53763441
[61] 0.53763441 0.54838710 0.54838710 0.55913978 0.56989247 0.58064516
[67] 0.59139785 0.60215054 0.60215054 0.61290323 0.62365591 0.63440860
[73] 0.64516129 0.65591398 0.66666667 0.66666667 0.67741935 0.68817204
[79] 0.69892473 0.70967742 0.70967742 0.72043011 0.73118280 0.74193548
[85] 0.75268817 0.75268817 0.76344086 0.77419355 0.78494624 0.79569892
[91] 0.80645161 0.81720430 0.82795699 0.82795699 0.83870968 0.84946237
[97] 0.84946237 0.84946237 0.84946237 0.84946237 0.84946237 0.84946237
[103] 0.84946237 0.84946237 0.84946237 0.84946237 0.84946237 0.84946237
[109] 0.84946237 0.84946237 0.84946237 0.84946237 0.84946237 0.84946237
[115] 0.84946237 0.84946237 0.84946237 0.84946237 0.84946237 0.84946237
[121] 0.84946237 0.84946237 0.84946237 0.84946237 0.84946237 0.84946237
[127] 0.84946237 0.86021505 0.86021505 0.86021505 0.86021505 0.86021505
[133] 0.87096774 0.87096774 0.87096774 0.87096774 0.87096774 0.88172043
[139] 0.89247312 0.89247312 0.89247312 0.89247312 0.89247312 0.89247312
[145] 0.90322581 0.91397849 0.91397849 0.91397849 0.91397849 0.92473118
[151] 0.92473118 0.92473118 0.93548387 0.93548387 0.93548387 0.93548387
[157] 0.94623656 0.94623656 0.94623656 0.94623656 0.94623656 0.94623656
[163] 0.94623656 0.94623656 0.94623656 0.94623656 0.94623656 0.94623656
[169] 0.94623656 0.95698925 0.95698925 0.95698925 0.95698925 0.95698925
[175] 0.95698925 0.95698925 0.96774194 0.96774194 0.96774194 0.96774194
[181] 0.96774194 0.96774194 0.96774194 0.96774194 0.96774194 0.96774194
[187] 0.96774194 0.96774194 0.96774194 0.96774194 0.96774194 0.96774194
[193] 0.96774194 0.96774194 0.96774194 0.96774194 0.96774194 0.97849462
[199] 0.98924731 0.98924731 1.00000000
Slot "alpha.values":
[[1]]
[1] Inf 0.991096434 0.984667270 0.984599159 0.983494405 0.970641299
[7] 0.959417835 0.945548941 0.943432189 0.938583020 0.932159806 0.930846938
[13] 0.912325837 0.911723615 0.907651100 0.905121019 0.890172812 0.890078186
[19] 0.885179651 0.883431431 0.879459891 0.876086217 0.868751832 0.868331219
[25] 0.865639036 0.858970526 0.858876675 0.844415442 0.842974300 0.835981859
[31] 0.834803976 0.814586047 0.806543942 0.790240205 0.785213140 0.781781371
[37] 0.779771989 0.773336236 0.772728821 0.770178504 0.760726142 0.757364019
[43] 0.757325590 0.748438143 0.746588080 0.745110673 0.744769966 0.739554341
[49] 0.728536415 0.717845453 0.716680598 0.715459280 0.714985914 0.708412104
[55] 0.703885141 0.703293499 0.701561487 0.700501359 0.698826511 0.697235328
[61] 0.696702150 0.694457482 0.689075677 0.665444679 0.663367560 0.658692553
[67] 0.657732644 0.642933593 0.636728451 0.628095575 0.627012496 0.623494622
[73] 0.620501132 0.612547843 0.606960209 0.605235403 0.598162949 0.589909284
[79] 0.586857799 0.579511087 0.576836208 0.567043171 0.547983407 0.543533783
[85] 0.540221346 0.539086009 0.537336015 0.537091350 0.536339509 0.531958184
[91] 0.531464015 0.531006532 0.529402244 0.522384507 0.517308606 0.501489336
[97] 0.499788081 0.496513160 0.492596896 0.491735594 0.490119891 0.488179708
[103] 0.480100183 0.470206008 0.468610247 0.463227453 0.461150807 0.458674210
[109] 0.448687336 0.448484671 0.439399995 0.432136142 0.429650397 0.423739359
[115] 0.419560072 0.408939895 0.402801992 0.393378108 0.392173971 0.385240464
[121] 0.384895941 0.383807972 0.380396459 0.378092079 0.371936985 0.370549294
[127] 0.364288579 0.364270971 0.362693564 0.360180429 0.360168796 0.353777439
[133] 0.353281048 0.349540913 0.348213542 0.340078180 0.336592126 0.336315317
[139] 0.326672910 0.319672178 0.310718619 0.300973098 0.292368449 0.288258273
[145] 0.277656869 0.268138293 0.265686095 0.259278968 0.257402979 0.253271061
[151] 0.248707470 0.248500489 0.244415489 0.240911145 0.239143340 0.233160827
[157] 0.230157183 0.212404891 0.212014560 0.211378771 0.195097957 0.194398425
[163] 0.180631658 0.172741714 0.161874325 0.151350957 0.140291078 0.138387070
[169] 0.134794140 0.133257805 0.126480399 0.123504905 0.122284044 0.120604738
[175] 0.120473353 0.118555284 0.110241034 0.107031842 0.105722115 0.101699993
[181] 0.090988280 0.088450984 0.086546283 0.085993218 0.084254795 0.083685883
[187] 0.083048377 0.081439129 0.072369921 0.060413627 0.059045866 0.050999138
[193] 0.040906997 0.035815400 0.030235062 0.018527600 0.016694412 0.014823599
[199] 0.012653524 0.007746305 0.005422562
ROCR documentation built on May 2, 2020, 5:05 p.m.
R Package Documentation
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Description Usage Arguments Author(s) References See Also Examples
Description
This is the method to plot all objects of class performance.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | ## S4 method for signature 'performance,missing'
plot(
x,
y,
...,
avg = "none",
spread.estimate = "none",
spread.scale = 1,
show.spread.at = c(),
colorize = FALSE,
colorize.palette = rev(rainbow(256, start = 0, end = 4/6)),
colorkey = colorize,
colorkey.relwidth = 0.25,
colorkey.pos = "right",
print.cutoffs.at = c(),
cutoff.label.function = function(x) { round(x, 2) },
downsampling = 0,
add = FALSE
)
## S3 method for class 'performance'
plot(...)
|
Arguments
x |
an object of class |
y |
not used |
... |
Optional graphical parameters to adjust different components of
the performance plot. Parameters are directed to their target component by
prefixing them with the name of the component ( |
avg |
If the performance object describes several curves (from
cross-validation runs or bootstrap evaluations of one particular method),
the curves from each of the runs can be averaged. Allowed values are
|
spread.estimate |
When curve averaging is enabled, the variation around
the average curve can be visualized as standard error bars
( |
spread.scale |
For |
show.spread.at |
For vertical averaging, this vector determines the x positions for which the spread estimates should be visualized. In contrast, for horizontal and threshold averaging, the y positions and cutoffs are determined, respectively. By default, spread estimates are shown at 11 equally spaced positions. |
colorize |
This logical determines whether the curve(s) should be colorized according to cutoff. |
colorize.palette |
If curve colorizing is enabled, this determines the color palette onto which the cutoff range is mapped. |
colorkey |
If true, a color key is drawn into the 4% border
region (default of |
colorkey.relwidth |
Scalar between 0 and 1 that determines the fraction of the 4% border region that is occupied by the colorkey. |
colorkey.pos |
Determines if the colorkey is drawn vertically at
the |
print.cutoffs.at |
This vector specifies the cutoffs which should be printed as text along the curve at the corresponding curve positions. |
cutoff.label.function |
By default, cutoff annotations along the curve
or at the color key are rounded to two decimal places before printing.
Using a custom |
downsampling |
ROCR can efficiently compute most performance measures even for data sets with millions of elements. However, plotting of large data sets can be slow and lead to PS/PDF documents of considerable size. In that case, performance curves that are indistinguishable from the original can be obtained by using only a fraction of the computed performance values. Values for downsampling between 0 and 1 indicate the fraction of the original data set size to which the performance object should be downsampled, integers above 1 are interpreted as the actual number of performance values to which the curve(s) should be downsampled. |
add |
If |
Author(s)
Tobias Sing tobias.sing@gmail.com, Oliver Sander osander@gmail.com
References
A detailed list of references can be found on the ROCR homepage at http://rocr.bioinf.mpi-sb.mpg.de.
See Also
prediction,
performance,
prediction-class,
performance-class
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | # plotting a ROC curve:
library(ROCR)
data(ROCR.simple)
pred <- prediction( ROCR.simple$predictions, ROCR.simple$labels )
pred
perf <- performance( pred, "tpr", "fpr" )
perf
plot( perf )
# To entertain your children, make your plots nicer
# using ROCR's flexible parameter passing mechanisms
# (much cheaper than a finger painting set)
par(bg="lightblue", mai=c(1.2,1.5,1,1))
plot(perf, main="ROCR fingerpainting toolkit", colorize=TRUE,
xlab="Mary's axis", ylab="", box.lty=7, box.lwd=5,
box.col="gold", lwd=17, colorkey.relwidth=0.5, xaxis.cex.axis=2,
xaxis.col='blue', xaxis.col.axis="blue", yaxis.col='green', yaxis.cex.axis=2,
yaxis.at=c(0,0.5,0.8,0.85,0.9,1), yaxis.las=1, xaxis.lwd=2, yaxis.lwd=3,
yaxis.col.axis="orange", cex.lab=2, cex.main=2)
|
Example output
Loading required package: gplots
Attaching package: 'gplots'
The following object is masked from 'package:stats':
lowess
An object of class "prediction"
Slot "predictions":
[[1]]
[1] 0.612547843 0.364270971 0.432136142 0.140291078 0.384895941 0.244415489
[7] 0.970641299 0.890172812 0.781781371 0.868751832 0.716680598 0.360168796
[13] 0.547983407 0.385240464 0.423739359 0.101699993 0.628095575 0.744769966
[19] 0.657732644 0.490119891 0.072369921 0.172741714 0.105722115 0.890078186
[25] 0.945548941 0.984667270 0.360180429 0.448687336 0.014823599 0.543533783
[31] 0.292368449 0.701561487 0.715459280 0.714985914 0.120604738 0.319672178
[37] 0.911723615 0.757325590 0.090988280 0.529402244 0.257402979 0.589909284
[43] 0.708412104 0.326672910 0.086546283 0.879459891 0.362693564 0.230157183
[49] 0.779771989 0.876086217 0.353281048 0.212014560 0.703293499 0.689075677
[55] 0.627012496 0.240911145 0.402801992 0.134794140 0.120473353 0.665444679
[61] 0.536339509 0.623494622 0.885179651 0.353777439 0.408939895 0.265686095
[67] 0.932159806 0.248500489 0.858876675 0.491735594 0.151350957 0.694457482
[73] 0.496513160 0.123504905 0.499788081 0.310718619 0.907651100 0.340078180
[79] 0.195097957 0.371936985 0.517308606 0.419560072 0.865639036 0.018527600
[85] 0.539086009 0.005422562 0.772728821 0.703885141 0.348213542 0.277656869
[91] 0.458674210 0.059045866 0.133257805 0.083685883 0.531958184 0.429650397
[97] 0.717845453 0.537091350 0.212404891 0.930846938 0.083048377 0.468610247
[103] 0.393378108 0.663367560 0.349540913 0.194398425 0.844415442 0.959417835
[109] 0.211378771 0.943432189 0.598162949 0.834803976 0.576836208 0.380396459
[115] 0.161874325 0.912325837 0.642933593 0.392173971 0.122284044 0.586857799
[121] 0.180631658 0.085993218 0.700501359 0.060413627 0.531464015 0.084254795
[127] 0.448484671 0.938583020 0.531006532 0.785213140 0.905121019 0.748438143
[133] 0.605235403 0.842974300 0.835981859 0.364288579 0.492596896 0.488179708
[139] 0.259278968 0.991096434 0.757364019 0.288258273 0.773336236 0.040906997
[145] 0.110241034 0.760726142 0.984599159 0.253271061 0.697235328 0.620501132
[151] 0.814586047 0.300973098 0.378092079 0.016694412 0.698826511 0.658692553
[157] 0.470206008 0.501489336 0.239143340 0.050999138 0.088450984 0.107031842
[163] 0.746588080 0.480100183 0.336592126 0.579511087 0.118555284 0.233160827
[169] 0.461150807 0.370549294 0.770178504 0.537336015 0.463227453 0.790240205
[175] 0.883431431 0.745110673 0.007746305 0.012653524 0.868331219 0.439399995
[181] 0.540221346 0.567043171 0.035815400 0.806543942 0.248707470 0.696702150
[187] 0.081439129 0.336315317 0.126480399 0.636728451 0.030235062 0.268138293
[193] 0.983494405 0.728536415 0.739554341 0.522384507 0.858970526 0.383807972
[199] 0.606960209 0.138387070
Slot "labels":
[[1]]
[1] 1 1 0 0 0 1 1 1 1 0 1 0 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0 1 1 0 1 1 1 0 0 1
[38] 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 0 0 0 1 0 1 0 0 1 0 0
[75] 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 0 1 0 0 1 0 0 1 1
[112] 1 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 1 1 0 1 0 1 0 1 1
[149] 1 1 1 0 0 0 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 0
[186] 0 0 1 0 0 0 1 0 1 1 0 1 0 1 0
Levels: 0 < 1
Slot "cutoffs":
[[1]]
[1] Inf 0.991096434 0.984667270 0.984599159 0.983494405 0.970641299
[7] 0.959417835 0.945548941 0.943432189 0.938583020 0.932159806 0.930846938
[13] 0.912325837 0.911723615 0.907651100 0.905121019 0.890172812 0.890078186
[19] 0.885179651 0.883431431 0.879459891 0.876086217 0.868751832 0.868331219
[25] 0.865639036 0.858970526 0.858876675 0.844415442 0.842974300 0.835981859
[31] 0.834803976 0.814586047 0.806543942 0.790240205 0.785213140 0.781781371
[37] 0.779771989 0.773336236 0.772728821 0.770178504 0.760726142 0.757364019
[43] 0.757325590 0.748438143 0.746588080 0.745110673 0.744769966 0.739554341
[49] 0.728536415 0.717845453 0.716680598 0.715459280 0.714985914 0.708412104
[55] 0.703885141 0.703293499 0.701561487 0.700501359 0.698826511 0.697235328
[61] 0.696702150 0.694457482 0.689075677 0.665444679 0.663367560 0.658692553
[67] 0.657732644 0.642933593 0.636728451 0.628095575 0.627012496 0.623494622
[73] 0.620501132 0.612547843 0.606960209 0.605235403 0.598162949 0.589909284
[79] 0.586857799 0.579511087 0.576836208 0.567043171 0.547983407 0.543533783
[85] 0.540221346 0.539086009 0.537336015 0.537091350 0.536339509 0.531958184
[91] 0.531464015 0.531006532 0.529402244 0.522384507 0.517308606 0.501489336
[97] 0.499788081 0.496513160 0.492596896 0.491735594 0.490119891 0.488179708
[103] 0.480100183 0.470206008 0.468610247 0.463227453 0.461150807 0.458674210
[109] 0.448687336 0.448484671 0.439399995 0.432136142 0.429650397 0.423739359
[115] 0.419560072 0.408939895 0.402801992 0.393378108 0.392173971 0.385240464
[121] 0.384895941 0.383807972 0.380396459 0.378092079 0.371936985 0.370549294
[127] 0.364288579 0.364270971 0.362693564 0.360180429 0.360168796 0.353777439
[133] 0.353281048 0.349540913 0.348213542 0.340078180 0.336592126 0.336315317
[139] 0.326672910 0.319672178 0.310718619 0.300973098 0.292368449 0.288258273
[145] 0.277656869 0.268138293 0.265686095 0.259278968 0.257402979 0.253271061
[151] 0.248707470 0.248500489 0.244415489 0.240911145 0.239143340 0.233160827
[157] 0.230157183 0.212404891 0.212014560 0.211378771 0.195097957 0.194398425
[163] 0.180631658 0.172741714 0.161874325 0.151350957 0.140291078 0.138387070
[169] 0.134794140 0.133257805 0.126480399 0.123504905 0.122284044 0.120604738
[175] 0.120473353 0.118555284 0.110241034 0.107031842 0.105722115 0.101699993
[181] 0.090988280 0.088450984 0.086546283 0.085993218 0.084254795 0.083685883
[187] 0.083048377 0.081439129 0.072369921 0.060413627 0.059045866 0.050999138
[193] 0.040906997 0.035815400 0.030235062 0.018527600 0.016694412 0.014823599
[199] 0.012653524 0.007746305 0.005422562
Slot "fp":
[[1]]
[1] 0 0 0 0 1 1 2 3 3 3 3 3 3 3 4 4 4 4
[19] 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5
[37] 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 8
[55] 9 9 9 9 9 9 10 10 11 11 11 11 11 11 12 12 12 12
[73] 12 12 12 13 13 13 13 13 14 14 14 14 14 15 15 15 15 15
[91] 15 15 15 16 16 16 17 18 19 20 21 22 23 24 25 26 27 28
[109] 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
[127] 47 47 48 49 50 51 51 52 53 54 55 55 55 56 57 58 59 60
[145] 60 60 61 62 63 63 64 65 65 66 67 68 68 69 70 71 72 73
[163] 74 75 76 77 78 79 80 80 81 82 83 84 85 86 86 87 88 89
[181] 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 106
[199] 106 107 107
Slot "tp":
[[1]]
[1] 0 1 2 3 3 4 4 4 5 6 7 8 9 10 10 11 12 13 14 15 16 17 17 18 19
[26] 20 21 22 23 24 25 26 27 28 29 30 30 31 32 33 33 34 35 36 37 38 39 40 41 42
[51] 43 44 45 45 45 46 47 48 49 50 50 51 51 52 53 54 55 56 56 57 58 59 60 61 62
[76] 62 63 64 65 66 66 67 68 69 70 70 71 72 73 74 75 76 77 77 78 79 79 79 79 79
[101] 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79
[126] 79 79 80 80 80 80 80 81 81 81 81 81 82 83 83 83 83 83 83 84 85 85 85 85 86
[151] 86 86 87 87 87 87 88 88 88 88 88 88 88 88 88 88 88 88 88 89 89 89 89 89 89
[176] 89 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 91 92 92
[201] 93
Slot "tn":
[[1]]
[1] 107 107 107 107 106 106 105 104 104 104 104 104 104 104 103 103 103 103
[19] 103 103 103 103 102 102 102 102 102 102 102 102 102 102 102 102 102 102
[37] 101 101 101 101 100 100 100 100 100 100 100 100 100 100 100 100 100 99
[55] 98 98 98 98 98 98 97 97 96 96 96 96 96 96 95 95 95 95
[73] 95 95 95 94 94 94 94 94 93 93 93 93 93 92 92 92 92 92
[91] 92 92 92 91 91 91 90 89 88 87 86 85 84 83 82 81 80 79
[109] 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61
[127] 60 60 59 58 57 56 56 55 54 53 52 52 52 51 50 49 48 47
[145] 47 47 46 45 44 44 43 42 42 41 40 39 39 38 37 36 35 34
[163] 33 32 31 30 29 28 27 27 26 25 24 23 22 21 21 20 19 18
[181] 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 1
[199] 1 0 0
Slot "fn":
[[1]]
[1] 93 92 91 90 90 89 89 89 88 87 86 85 84 83 83 82 81 80 79 78 77 76 76 75 74
[26] 73 72 71 70 69 68 67 66 65 64 63 63 62 61 60 60 59 58 57 56 55 54 53 52 51
[51] 50 49 48 48 48 47 46 45 44 43 43 42 42 41 40 39 38 37 37 36 35 34 33 32 31
[76] 31 30 29 28 27 27 26 25 24 23 23 22 21 20 19 18 17 16 16 15 14 14 14 14 14
[101] 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14
[126] 14 14 13 13 13 13 13 12 12 12 12 12 11 10 10 10 10 10 10 9 8 8 8 8 7
[151] 7 7 6 6 6 6 5 5 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4
[176] 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 1 1
[201] 0
Slot "n.pos":
[[1]]
[1] 93
Slot "n.neg":
[[1]]
[1] 107
Slot "n.pos.pred":
[[1]]
[1] 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
[19] 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
[37] 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53
[55] 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71
[73] 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89
[91] 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107
[109] 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125
[127] 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143
[145] 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161
[163] 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179
[181] 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197
[199] 198 199 200
Slot "n.neg.pred":
[[1]]
[1] 200 199 198 197 196 195 194 193 192 191 190 189 188 187 186 185 184 183
[19] 182 181 180 179 178 177 176 175 174 173 172 171 170 169 168 167 166 165
[37] 164 163 162 161 160 159 158 157 156 155 154 153 152 151 150 149 148 147
[55] 146 145 144 143 142 141 140 139 138 137 136 135 134 133 132 131 130 129
[73] 128 127 126 125 124 123 122 121 120 119 118 117 116 115 114 113 112 111
[91] 110 109 108 107 106 105 104 103 102 101 100 99 98 97 96 95 94 93
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[127] 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57
[145] 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39
[163] 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21
[181] 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3
[199] 2 1 0
An object of class "performance"
Slot "x.name":
[1] "False positive rate"
Slot "y.name":
[1] "True positive rate"
Slot "alpha.name":
[1] "Cutoff"
Slot "x.values":
[[1]]
[1] 0.000000000 0.000000000 0.000000000 0.000000000 0.009345794 0.009345794
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[193] 0.953271028 0.962616822 0.971962617 0.981308411 0.990654206 0.990654206
[199] 0.990654206 1.000000000 1.000000000
Slot "y.values":
[[1]]
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[199] 0.98924731 0.98924731 1.00000000
Slot "alpha.values":
[[1]]
[1] Inf 0.991096434 0.984667270 0.984599159 0.983494405 0.970641299
[7] 0.959417835 0.945548941 0.943432189 0.938583020 0.932159806 0.930846938
[13] 0.912325837 0.911723615 0.907651100 0.905121019 0.890172812 0.890078186
[19] 0.885179651 0.883431431 0.879459891 0.876086217 0.868751832 0.868331219
[25] 0.865639036 0.858970526 0.858876675 0.844415442 0.842974300 0.835981859
[31] 0.834803976 0.814586047 0.806543942 0.790240205 0.785213140 0.781781371
[37] 0.779771989 0.773336236 0.772728821 0.770178504 0.760726142 0.757364019
[43] 0.757325590 0.748438143 0.746588080 0.745110673 0.744769966 0.739554341
[49] 0.728536415 0.717845453 0.716680598 0.715459280 0.714985914 0.708412104
[55] 0.703885141 0.703293499 0.701561487 0.700501359 0.698826511 0.697235328
[61] 0.696702150 0.694457482 0.689075677 0.665444679 0.663367560 0.658692553
[67] 0.657732644 0.642933593 0.636728451 0.628095575 0.627012496 0.623494622
[73] 0.620501132 0.612547843 0.606960209 0.605235403 0.598162949 0.589909284
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[85] 0.540221346 0.539086009 0.537336015 0.537091350 0.536339509 0.531958184
[91] 0.531464015 0.531006532 0.529402244 0.522384507 0.517308606 0.501489336
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[103] 0.480100183 0.470206008 0.468610247 0.463227453 0.461150807 0.458674210
[109] 0.448687336 0.448484671 0.439399995 0.432136142 0.429650397 0.423739359
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[127] 0.364288579 0.364270971 0.362693564 0.360180429 0.360168796 0.353777439
[133] 0.353281048 0.349540913 0.348213542 0.340078180 0.336592126 0.336315317
[139] 0.326672910 0.319672178 0.310718619 0.300973098 0.292368449 0.288258273
[145] 0.277656869 0.268138293 0.265686095 0.259278968 0.257402979 0.253271061
[151] 0.248707470 0.248500489 0.244415489 0.240911145 0.239143340 0.233160827
[157] 0.230157183 0.212404891 0.212014560 0.211378771 0.195097957 0.194398425
[163] 0.180631658 0.172741714 0.161874325 0.151350957 0.140291078 0.138387070
[169] 0.134794140 0.133257805 0.126480399 0.123504905 0.122284044 0.120604738
[175] 0.120473353 0.118555284 0.110241034 0.107031842 0.105722115 0.101699993
[181] 0.090988280 0.088450984 0.086546283 0.085993218 0.084254795 0.083685883
[187] 0.083048377 0.081439129 0.072369921 0.060413627 0.059045866 0.050999138
[193] 0.040906997 0.035815400 0.030235062 0.018527600 0.016694412 0.014823599
[199] 0.012653524 0.007746305 0.005422562
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